Journal of Petroleum Science and Engineering 106 (2013) 1–8

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Journal of Petroleum Science and Engineering

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asolaim

journal homepage: www.elsevier.com/locate/petrol

An experimental study on factors affecting the heavy crude oilin water emulsions viscosity

Masood Azodi, Ali Reza Solaimany Nazar n

University of Isfahan, Department of Chemical Engineering, Isfahan, Iran

a r t i c l e i n f o

Article history:Received 13 January 2012Accepted 19 April 2013Available online 30 April 2013

Keywords:oil in water emulsionviscosityrheological equationTaguchi method

05/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.petrol.2013.04.002

esponding author. Tel.: +98 311 7934027; fax:ail addresses: asolaimany@eng.ui.ac.ir,any@yahoo.com (A.R. Solaimany Nazar).

a b s t r a c t

In this article the factors affecting two heavy crude oil types in water emulsion viscosity through theTaguchi method are studied. The factors of oil concentration, emulsifier concentration and temperaturehave the greatest impact on the viscosity of emulsions of the two heavy oil types. With an increase in oilconcentration and emulsifier concentration, the viscosity increases, while with an increase in tempera-ture the viscosity decreases. A modified rheological equation is introduced for predicting the viscosity ofoil in water emulsion based on the factors affecting viscosity. This equation is developed based on shearrate, oil concentration, emulsifier concentration and temperature. In comparison with the two existingrheological equations this developed equation fits better with viscosity of emulsions of both oil typesexperimental results. The coefficients of the modified equation give a better estimate of the effects ofdiscussed factors.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Viscosity of heavy crude oil types is very high and is not suitablefor pipeline transportation. Having a balanced amount of heavycrude oil in water emulsion is a suitable method for reducing theviscosity for pipeline transportation. In the previous studies, theeffects of miscellaneous factors such as oil concentration, emulsifierconcentration, mixing speed, salinity, pH, temperature and shearrate on viscosity of oil in water emulsions are investigated (Zaki,1997; Ahmed et al., 1999; Yaghi and al-Bemani, 2002; Ashrafizadeet al., 2010). There exists a direct relation between oil concentrationincrease and the number of oil droplets which in fact increases theviscosity of emulsion. Increasing emulsifier concentration and mix-ing speed reduces average oil droplets size leading to an increase ofthe viscosity of oil in water emulsion. Studies on the effect of salinityon the viscosity of oil inwater emulsions disclosed that the emulsionviscosity increases with an increase in salinity (Ahmed et al., 1999;Ashrafizade et al., 2010). Ashrafizade et al. (2010) showed that thepH has little effect on the viscosity of oil in water emulsions. Anincrease in temperature often reduces the viscosity of emulsionsfollowing an exponential type trend. Concentrated oil in wateremulsions often behave like pseudo-plastic fluid, i.e. the viscositydecreases with an increase in shear rate (Pal and Rhodes, 1989).

ll rights reserved.

+98 311 7934031.

A common approach to optimize operating parameters of aparticular process is to perform all or some of the possible experi-ments employing one at a time, i.e. varying a parameter whilekeeping the others constant, or trial and error methods with thedesign variables to find a feasible or optimum condition. A fullfactorial design needed too many experiments. Such an approachmay be time consuming and expensive when multiple factors areinvolved. The technique for the determination and investigation ofthe influential experiment parameters at different levels is called the‘design’ of the experiment. This technique aims to discover thecombinations of factors that give the best combination. However,employing a full factorial experimental design is restricted whenmany factors and levels are studied. Analysis of variance (ANOVA)was used to analyze the results of the experiments and to determinethe contribution of each influencing factor. In this respect, theTaguchi experimental design method can reduce the number ofexperiments to study the effects of multiple variables simultaneouslywhile retaining data collection quality. The Taguchi method alsoscreens the significant factors affecting the response from those withinsignificance and gives the optimum condition to attain the mostdesirable performance (Roy, 2001).

In the previous studies, the quantitative effects of factors onviscosity of the emulsion are not considered. The flow properties ofconcentrated emulsions are of interest in many applications. Forexample, mixing equipment design for emulsion production dependson the rheological properties of emulsions. Viscosity of fluid is animportant parameter in determining the pressure drop along pipe-line and its size. Predicting viscosity of oil in water emulsion requiresknowledge of the dependence of emulsion viscosity with effective

Table 3Selected factors and their levels.

Factors Symbols Levels

1 2 3

1 Emulsifier concentration (wt%) A 1 2.5 4

M. Azodi, A.R. Solaimany Nazar / Journal of Petroleum Science and Engineering 106 (2013) 1–82

factors such as shear rate and concentration of oil (Binks, 1998).Previous studies have mostly focused on dispersed phase concentra-tion, temperature and shear rate effects for developing an equationin order to predict emulsion viscosity (Sherman, 1962; Pal andRhodes, 1989; Rønningsen, 1995; al-Roomi et al., 2004).

This study intends to investigate the effects of shear rate, oilconcentration, emulsifier concentration, temperature and interac-tions on the viscosity of oil in water emulsions using the Taguchimethod while developing a modified equation for predictingviscosity of heavy oil–water emulsion as a main tool for transpor-tation pipeline designing.

2. Experimental

2.1. Material

Two sample of heavy oil types are used in this study. MondMount heavy crude oil (type 1) is from the oil fields in south of Iranand oil type 2 is a mixture of bitumen and diesel oil with 80:20volume ratio. Some specifications of these oil types are listed inTable 1. Emulsifiers Triton X-100, NP10 and KENON40 were used toprepare emulsions. Some of the specifications of these emulsifiersare presented in Table 2. To adjust the salinity of solution, sodiumchloride a Merck product with laboratory purity is used.

2.2. Design of experiments

Determining the factors and their levels is the first phase indesigning the experiments. Based on the previous studies six factorsare selected. These factors and their levels are introduced in Table 3.In addition to the above mentioned factors, three possible interactionsbetween emulsifier concentration and emulsifier type (A�B), emul-sifier concentration and concentration of crude oil (A�C), emulsifierconcentration and salinity (A�D) are included in Table 4. By usingMINITAB software for this quantity of factors and interactions finallyL27 Taguchi orthogonal experiment table is selected (Table 5). Thistable shows the 27 run tests. Each row of this table represents onetest at a specified condition.

2.3. Preparation of emulsion

The emulsifier and sodium chloride are dissolved in distilledwater under mild stirring condition. Heavy oil is heated to 60 1C

Table 1Specification of heavy crude oil samples.

Oiltypes

APIgravity

Kinematic viscosity(mm2/s) at 100 1C

Dynamic viscosity (cp) at 40 1C

Shear rate(s−1)

100 200 500 1000

Oil 1 16 79.531 4520 4190 3650 3330Oil 2 20 66.76 4710 4250 3320 2790

Table 2Specification of emulsifiers.

Specifications KENON40

Type NonionicChemical structure C9H19(C6H4)(OC2H4)40OHHLB 17.8Company Kimiagaran emrooz

and is gradually added to the premade solution where it is mixedwith an IKA mechanical mixer model RW 20 D, with a four bladestainless steel propeller type stirrer for 30 min. To prepare thesecond oil sample, bitumen and diesel are mixed for several hoursuntil the mixture is completely homogenized.

2.4. Viscosity determination

This prepared emulsion is used for measuring the viscosity. TheAnton Paar viscometer model Rheolab QC is used for measuringthe viscosity. The concept of measuring is based on concentricrotating cylinders. This device is capable of measuring the viscos-ity based on shear rate. Water bath thermostat allows for deter-mining viscosity value at different temperatures.

3. Results and discussions

Experiments based on Taguchi L27 table tests are performed.Viscosity of emulsions of both the heavy oil types at shear rates100, 200, 500 and 1000 (s−1) as a function of the emulsifier typeare presented in Table 6. In a recent research the effects of variousoperating factors on the stability of two heavy oil types in wateremulsions are investigated (Azodi and Solaimany Nazar, 2013). Thestability is measured based on the amount of separated water ofemulsion after 24 h. It is shown that the stability is increased by anincrease in oil content and the emulsifier concentration. Anincrease in the salinity and mixing speed leads to an increase inthe stability of emulsion.

3.1. Analysis of variance of viscosity results

The analysis of variance of viscosity results are presented inTables 7–10. These results are obtained using MINITABs Release 15software. Important statistical terms such as DF (degree of freedom),

NP10 Triton X-100

Nonionic NonionicC9H19(C6H4)(OC2H4)10OH C8H17(C6H4)(OC2H4)10OH13.6 13.5Sigma-Aldrich Merck

2 Type of emulsifier B Triton X-100 NP10 KENON403 Oil concentration (vol%) C 40 55 704 Salinity (ppm) D 10,000 40,000 70,0005 Speed of mixing (rpm) E 1000 1500 20006 Temperature (1C) F 20 40 60

Table 4Selected interactions.

Interactions Symbols

1 Emulsifier concentration (A) and emulsifier type (B) A�B2 Emulsifier concentration (A) and oil concentration (C) A�C3 Emulsifier concentration (A) and salinity (D) A�D

Table 5L27 Taguchi orthogonal array of designed experiments based on the coded levels.

Run Emulsifierconcentration

Type ofemulsifier

Oilconcentration

Salinity Speedof mixing

Temperature

1 1 1 1 1 1 12 1 1 2 2 2 23 1 1 3 3 3 34 1 2 1 2 3 35 1 2 2 3 1 16 1 2 3 1 2 27 1 3 1 3 2 28 1 3 2 1 3 39 1 3 3 2 1 1

10 2 1 1 1 1 211 2 1 2 2 2 312 2 1 3 3 3 113 2 2 1 2 3 114 2 2 2 3 1 215 2 2 3 1 2 316 2 3 1 3 2 317 2 3 2 1 3 118 2 3 3 2 1 219 3 1 1 1 1 320 3 1 2 2 2 121 3 1 3 3 3 222 3 2 1 2 3 223 3 2 2 3 1 324 3 2 3 1 2 125 3 3 1 3 2 126 3 3 2 1 3 227 3 3 3 2 1 3

M. Azodi, A.R. Solaimany Nazar / Journal of Petroleum Science and Engineering 106 (2013) 1–8 3

Adj MS (adjusted mean squares), F-ratio, P-value and residual errorfor each factor and interaction are presented. F-ratio is calculated bydividing the Adj MS of factor by Adj MS of the residual error. Thegreater the F-ratio of the factor (or interaction), the greater itsinfluence on the results. P-value is the smallest probability indicatingthat a factor (or an interaction) is not significant and its value isalways between 0 and 1. The residual error term combines the effectsof three sources: factors excluded from the experiment, uncontrol-lable factors and experimental error.

The analysis of variance of viscosity results of emulsions of oiltype 1 at 100, 200, 500 and 1000 (s−1) shear rates are presented inTables 7 and 8. Based on the obtained F-ratio, oil concentration (C)has the most influence on the viscosity results of emulsions of oiltype 1 at all shear rates. After oil concentration, the factors emulsifierconcentration and temperature have the most influence on theviscosity results of emulsions in oil type 1 at all shear rates. Theeffects of other factors and interaction on the emulsion viscosity arerelatively low.

The analysis of variance of viscosity results of emulsions of oiltype 2 at shear rates of 100, 200, 500 and 1000 (s−1) are presentedin Tables 9 and 10. Similar results are obtained for emulsions of oiltype 1. The oil concentration, emulsifier concentration and tem-perature factors have the most influence on the results of theviscosity of emulsions in oil type 2 at all shear rates. The effects ofthese three factors are used for the development of correlationthat would predict the oil viscosity in water emulsion.

3.2. Main effects

The main effect of oil concentration, temperature and emulsifierconcentration are obtained through MINITABs Release 15 software.The effect of an operating factor is obtained by plotting the factor-level results against the corresponding factor level. The plot makestwo pieces of information about the factor obvious to the experi-menter: the nature of the trend of influence of the factor to theresult as it changes from one level to another level and the variation

in results for the shift in factor levels proportional to the slope or thedifference between endpoints indicates the sensitivity of the factor'sresults (Roy, 2001). Each point on these plots presents the averagedata of nine experiments on the relevant level.

3.2.1. Effect of oil concentration on the viscosityThe effect of oil concentration on the viscosity of emulsions

of both the heavy oil types at shear rates of 100, 200, 500 and1000 (s−1) are shown in Figs. 1 and 2. As observed the emulsionviscosity increases with an increase in oil concentration. This isdue to an increase in the number of oil droplets; thus, thecontacting surface between the droplets increases. It should benoted that each point on these plots presents the average of nineexperimental data on the relevant level.

3.2.2. Effect of temperature on the viscosityThe effect of temperature on the viscosity of emulsions of both

the heavy oil types at shear rates of 100, 200, 500 and 1000 (s−1) isshown in Figs. 3 and 4. A temperature rise leads to a decrease inemulsion viscosity.

3.2.3. Effect of emulsifier concentration on the viscosityThe effect of emulsifier concentration on the viscosity of

emulsions of both the heavy oil types at shear rates of 100, 200,500 and 1000 (s−1) are presented in Figs. 5 and 6. With an increasein emulsifier concentration, droplets become smaller due to lowerinterfacial tension. With a decrease in droplet size, the overalldroplets contacting surface increases and consequently the emul-sion viscosity increases.

3.3. Developing correlation to predict the viscosity

3.3.1. Oil concentrationAs mentioned before, in the analysis of variance, the factors of

oil concentration, temperature and concentration of emulsifierhave the strongest influence on viscosity. These are used in thedeveloped correlation. The concentration dispersed phase orvolume fraction of the dispersed phase (ϕ) was used in developingmany rheological equations to predict the viscosity of oil–wateremulsions (Sherman, 1962; Pal and Rhodes, 1989; Rønningsen,1995; al-Roomi et al., 2004). Broughton and Squires is the mostwidely used equation. This exponential equation predicts therelative viscosity (ηr) based on the volume fraction of the dispersedphase.

ηr∝A1eC1ϕ ð1ÞA1 and C1 are constants. The exponential behavior of emulsionviscosity with volume fraction of the dispersed phase wasapproved by many systems (Pal and Rhodes, 1989). Oil in wateremulsion relative viscosity (ηr) and emulsion viscosity (η) are equalbecause the viscosity of the continuous phase (water) is approxi-mately equal to one, namely

η∝A1eC1ϕ ð2Þ

3.3.2. TemperatureThe temperature factor was used for the development of some

rheological equations just like the volume fraction of the dispersedphase (Rønningsen, 1995; al-Roomi et al., 2004). The correlationbetween emulsion viscosity and temperature with the exponentialtype trend is in conformity with many emulsion systems (Johnsenand Rønningsen, 2003; al-Roomi et al., 2004).

η∝A2eC2=T ð3Þ

Table 6Viscosity results according to the Taguchi L27 for emulsions of both oil types at 100, 200, 500 and 1000 (s−1) shear rates.

Run Type of emulsifier Viscosity (cp)

Emulsions of oil type 1 (s−1) Emulsions of oil type 2 (s−1)

100 200 500 1000 100 200 500 1000

1 Triton X-100 8.99 7.24 7.75 11 150 137 64.6 28.82 Triton X-100 30.9 13.5 10.1 15 155 114 54.2 20.73 Triton X-100 45.1 35.2 30.7 30.2 112 86.9 56 44.14 NP10 5.06 4.97 3.44 4.49 2.03 2.49 3.47 4.835 NP10 12.3 13.9 16.4 16.5 147 117 66 44.36 NP10 56.2 42.9 57.3 55.1 183 125 85.9 78.27 KENON40 14.1 12.2 8.62 8.47 10 7.54 10.4 8.28 KENON40 40.1 16.7 31.2 14 23.7 18.4 14.9 37.49 KENON40 277 230 175 147 190 135 99.3 11010 Triton X-100 2.4 2.6 5.16 7.4 5.68 5.33 7.26 10.411 Triton X-100 106 82.9 43.3 32.1 105 71.7 44 40.412 Triton X-100 197 154 119 89.1 264 182 129 13513 NP10 2.67 4.11 7.09 9.08 6.69 7.44 13.8 11.414 NP10 12.3 7.03 7.84 11 90 63.5 37.5 29.915 NP10 160 117 74.5 52.3 177 142 93.7 74.416 KENON40 13.6 10.1 10.1 8.21 4.87 3.93 4.83 4.8717 KENON40 25.7 26.1 20.3 20.9 121 86.9 74.4 72.518 KENON40 242 188 130 94.3 170 133 95.2 76.419 Triton X-100 70.2 45.1 25.5 10.9 6.12 5.3 6.57 8.4320 Triton X-100 143 110 81.2 68.7 157 99.8 79.6 46.821 Triton X-100 256 202 143 120 381 265 175 10622 NP10 71.2 47.3 31.1 30.6 37.2 27.8 23.5 2123 NP10 97 74.2 51.5 20.1 123 97.3 82 54.124 NP10 431 327 233 215 275 197 132 21125 KENON40 40.1 39 23.7 20.3 8.1 8.49 14.1 17.526 KENON40 74.6 56.6 56.9 108 76 45.8 51.3 10927 KENON40 148 109 66.3 43.7 146 114 70.3 49

Table 7Analysis of variance of viscosity results of emulsions of oil type 1 at 100 and 200(s−1) shear rates.

Sources (symbols) DF 100 (s−1) 200 (s−1)

Adj MS F-ratio P-value Adj MS F-ratio P-value

A 2 20,482.6 5.11 0.164 11,533.1 4.29 0.189B 2 21.1 0.01 0.995 71.6 0.03 0.974C 2 78,171.1 19.5 0.049 47,768.3 17.75 0.053D 2 3185.5 0.79 0.557 1656.7 0.62 0.619E 2 2145.9 0.54 0.651 1223 0.45 0.687F 2 6545.1 1.63 0.38 5448.1 2.02 0.331A�B 4 9122.8 2.28 0.328 5326.6 1.98 0.363A�C 4 2241.7 0.56 0.721 1114.4 0.41 0.795A�D 4 4698.8 1.17 0.509 3001 1.12 0.523Residual error 2 4008.9 2690.5

Table 8Analysis of variance of viscosity results of emulsions of oil type 1 at 500 and 1000(s−1) shear rates.

Sources (symbols) DF 500 (s−1) 1000 (s−1)

Adj MS F-ratio P-value Adj MS F-ratio P-value

A 2 4278.2 3.31 0.232 3907.6 2.01 0.332B 2 93.5 0.07 0.932 184 0.09 0.914C 2 25,262.3 19.56 0.049 16,156.5 8.3 0.108D 2 557.8 0.43 0.698 856.9 0.44 0.694E 2 274.5 0.21 0.825 358.7 0.18 0.844F 2 3476 2.69 0.271 4113.3 2.11 0.321A�B 4 2785.6 2.16 0.341 1064.9 0.55 0.727A�C 4 319.1 0.25 0.891 423.3 0.22 0.908A�D 4 1589.3 1.23 0.494 2122.7 1.09 0.53Residual error 2 1291.2 1946.2

M. Azodi, A.R. Solaimany Nazar / Journal of Petroleum Science and Engineering 106 (2013) 1–84

where T is the absolute temperature (K) and A2 and C2 areconstants.

3.3.3. Emulsifier concentrationEmulsifier concentration is not used in developing rheological

equations yet, but it is intended to be used in developing amodified correlation. The main effect of emulsifier concentrationcurves (Figs. 5 and 6) fits well with the exponential equation;therefore, the correlation between viscosity of emulsion andemulsifier concentration is considered as follows:

η∝A3eC3ω ð4Þ

where ω is the emulsifier concentration (wt%) and A3 and C3 arethe constants.

3.3.4. Shear rateThe correlation between viscosity and shear rate is obtained by

applying the following well known power law equation:

η∝A4γn ð5Þ

where γ is the shear rate. A4 and n are the constants where n forpseudo-plastic fluid is negative.

The coefficient A4 in Eq. (5) is considered as a function ofvolume fraction of the dispersed phase (ϕ), the temperature andconcentration of emulsifier. Combining Eqs. (2)–(4), the constantA4 is obtained as follows:

A4 ¼ K1exp C1ϕþ C2

Tþ C3ω

� �ð6Þ

Table 9Analysis of variance of viscosity results of emulsions of oil type 2 at 100 and 200(s−1) shear rates.

Sources (symbols) DF 100 (s−1) 200 (s−1)

Adj MS F-ratio P-value Adj MS F-ratio P-value

A 2 2354.7 0.46 0.683 798.3 0.26 0.795B 2 9543.1 1.88 0.347 4774.4 1.54 0.393C 2 77,384.6 15.27 0.061 38,549.8 12.47 0.074D 2 863.3 0.17 0.854 445.2 0.14 0.874E 2 90.4 0.02 0.982 200 0.06 0.939F 2 11,006 2.17 0.315 5137.7 1.66 0.376A�B 4 1499.6 0.3 0.862 868.1 0.28 0.871A�C 4 4095.6 0.81 0.618 2620.7 0.85 0.604A�D 4 1713.2 0.34 0.837 918.8 0.3 0.861Residual error 2 5069.2 3091.9

Table 10Analysis of variance of viscosity results of emulsions of oil type 2 at 500 and 1000(s−1) shear rates.

Sources (symbols) DF 500 (s−1) 1000 (s−1)

Adj MS F-ratio P-value Adj MS F-ratio P-value

A 2 970.6 1.05 0.487 1758.1 6.1 0.141B 2 920.7 1 0.501 217.6 0.75 0.57C 2 17,297.8 18.74 0.051 16,486.5 57.19 0.017D 2 232.4 0.25 0.799 1870 6.49 0.134E 2 14.3 0.02 0.985 493.4 1.71 0.369F 2 2460.2 2.67 0.273 3647.8 12.65 0.073A�B 4 446.7 0.48 0.758 1035.6 3.59 0.229A�C 4 679.8 0.74 0.645 385.6 1.34 0.47A�D 4 412.4 0.45 0.777 1227.3 4.26 0.199Residual error 2 922.9 288.3

Fig. 1. Effect of oil concentration on viscosity of emulsions of oil type 1 at 100, 200,500 and 1000 (s−1) shear rates.

Fig. 2. Effect of oil concentration on viscosity of emulsions of oil type 2 at 100, 200,500 and 1000 (s−1) shear rates.

Fig. 3. Effect of temperature on viscosity of emulsions of oil type 1 at 100, 200, 500and 1000 (s−1) shear rates.

Fig. 4. Effect of temperature on viscosity of emulsions of oil type 2 at 100, 200, 500and 1000 (s−1) shear rates.

M. Azodi, A.R. Solaimany Nazar / Journal of Petroleum Science and Engineering 106 (2013) 1–8 5

With the replacement of the obtained A4 in Eq. (5) thefollowing modified emulsion viscosity equation is obtained:

η¼ K1γnexp C1ϕþ C2

Tþ C3ω

� �ð7Þ

where K1, n, C1, C2 and C3 are the constants and depend on theemulsion system.

3.4. Evaluation and validation of modified correlation

Rønningsen (1995) developed the following equation based onthe volume fraction of the dispersed phase and temperature in

Fig. 5. Effect of emulsifier concentration on viscosity of emulsions of oil type 1 at100, 200, 500 and 1000 (s−1) shear rates.

Fig. 6. Effect of emulsifier concentration on viscosity of emulsions of oil type 2 at100, 200, 500 and 1000 (s−1) shear rates.

M. Azodi, A.R. Solaimany Nazar / Journal of Petroleum Science and Engineering 106 (2013) 1–86

order to predict the viscosity of water in oil emulsions:

η¼ expðk1 þ k2T þ k3ϕþ k4ðT � ϕÞÞ ð8ÞJohnsen and Rønningsen (2003) compared the results of Eq. (8)

and models developed by Pal and Rhodes (1989), Pal (2000) andMooney (1951), with the experimental data of oil in water emul-sions of several North Sea crude oil types. They showed that therelative error of Eq. (8) at high concentrations of dispersed phase isless than that of the other models, even at low concentrations.

The Eq. (9) developed by al-Roomi et al. (2004) is based on thevolume fraction of the dispersed phase, temperature and shearrate for oil in water emulsion viscosity data. They showed that theequation with correlation coefficients (R) greater than 0.9 is a goodfit and this correlation gives the correct estimation of the variableeffect.

η¼ aγbexp cϕþ dT

� �ð9Þ

The objective of this study is to evaluate the modified Eq. (7). Theresults predicted by Eqs. (7)–(9) are compared here. The models fitthe viscosity results (Table 6) for each emulsion of both oil types andemulsifier types separately. Since there is no shear rate dependence

of viscosity in Eq. (8) (Rønningsen model), this model fits theviscosity data of oil type 1 emulsion at 100 and 1000 (s−1) shearrates (Table 11). The predicted results of al-Roomi and the modifiedmodels are presented in Tables 12 and 13, respectively.

The statistics R2, Adj-R2 and standard error are

R2 ¼ 1−∑ðyi−yiÞ2∑ðyi−yiÞ2

ð10Þ

Adj� R2 ¼ 1−p−1

p−ðmþ 1−rÞ ð1−R2Þ ð11Þ

and

Standard error¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑ðyi−yiÞ2

p

sð12Þ

where yi, yi and yi are the experimental and predicted results bythe regression model and the average of the experimental results,respectively. Here, p is the number of fitted data, m is the totalnumber of independent variables and r is the number of indepen-dent variables that are eliminated from the model (Montgomeryand Peck, 1982).

The R2 values obtained for Rønningsen model is relatively lowand the results do not fit well with this model. The Adj-R2 and R2

are almost different which indicates that the model containsvariables which have no significant effect on fitness. The R2 obtainedfor al-Roomi model shows that this model does not fit well with theresults. The R2 obtained for the modified model shows that thismodel fits well with the results of oil type 1 emulsion viscosity data.It does not fit within oil type 2 emulsion viscosity results betterthan that of the oil type 1 emulsion.

3.5. Validation of the results

One of the techniques in determining the validity of theregression model is analyzing the model coefficients and comparingthem with experimental results and the other models. The coeffi-cients with unexpected signs or great values often are referred to asthe regression models which are either unsuitable or poor inestimation of the effects of variables that have been carried out(Montgomery and Peck, 1982).

The sign of coefficient k2 in Rønningsen model is positive,and this indicates that the coefficient means of the viscosity increaseswith an increase in temperature. Experimental results (Figs. 3 and 4)show the viscosity always decreases with an increase in temperature.Consequently, experimental results are inconsistent with the sign ofk2 coefficient. Therefore, the Rønningsen model offers a poorestimation of the effect of temperature. The variance inflation factors(VIF) for the predictors of Rønningsen model are calculated throughMINITABs Release 15 software and are presented in Table 14.Predictors T and T�ϕ in the Rønningsen model have a VIF greaterthan 10 that refers to multi-co-linearity issue between the predictorsof the Rønningsen model and indicates that the coefficients of thepredictors are estimated poorly. Poor estimates of the coefficients ofthe individual variables of the model do not necessarily mean a poorfit. Here, to reduce multi-co-linearity, unimportant predictors shouldbe removed from the model (Montgomery and Peck, 1982); there-fore, the T�ϕ should be removed from the Rønningsen model.As observed, the VIF for the predictors in the al-Roomi equation andmodified equation is equal to one. If VIF is equal to one, there is nomulti-co-linearity between the predictors in regression equation(Montgomery and Peck, 1982). Consequently there is no multi-co-linearity between the predictors in al-Roomi model and modifiedequation.

The variation of coefficient a in al-Roomi model is calculatedwithin 0.00307oao69.449. This is a relatively high variation and

Table 11Correlated coefficient of the Rønningsen model with viscosity of emulsions of the heavy oil type 1 at 100 and 1000 (s−1) shear rates.

Emulsifiers Shear rates Correlated coefficient of Rønningsen model η¼ expðk1 þ k2T þ k3ϕþ k4ðT � ϕÞÞ R2 Adj-R2 Standard error

(s−1) k1 k2 k3 k4

Triton X-100 100 −0.553 0.061 9.118 −0.1134 0.619 0.492 51.221000 2.317 −0.0577 3.807 0.0605 0.713 0.617 20.44

NP10 100 −13.95 0.286 30.022 −0.482 0.808 0.744 56.381000 −8.859 0.166 21.81 −0.312 0.944 0.926 14.58

KENON40 100 −3.603 0.0541 13.619 −0.097 0.960 0.946 19.051000 −1.23 0.05 9.622 −0.107 0.711 0.615 26.1

Table 12Correlated coefficient of al-Roomi model with viscosity of emulsions of both the heavy oil types at 100, 200, 500 and 1000 (s−1) shear rates.

Oil types Emulsifiers Correlated coefficient of al-Roomi model η¼ aγbexpðcϕþ ðd=TÞÞ R2 Adj-R2 Standard error

a b c d

1 Triton X-100 12.85 −0.339 5.243 14.871 0.611 0.575 40.3NP10 0.00307 −0.322 15.642 46.842 0.866 0.853 34.66KENON40 0.918 −0.329 9.289 15.213 0.866 0.875 24.87

2 Triton X-100 69.449 −0.641 4.343 11.463 0.680 0.650 47.71NP10 11.335 −0.315 5.580 14.301 0.863 0.851 25.15KENON40 7.404 −0.293 5.822 11.066 0.831 0.815 21.8

Table 13Correlated coefficient of modified model with viscosity of emulsions of both the heavy oil types at 100, 200, 500 and 1000 (s−1) shear rates.

Oil types Emulsifiers Correlated coefficient of modified model η¼ K1γnexpðC1ϕþ ðC2=TÞ þ C3ωÞ R2 Adj-R2 Standard error

K1 n C1 C2 C3

1 Triton X-100 4.23 −0.345 5.422 11.277 0.408 0.946 0.939 14.97NP10 0.351 −0.344 8.602 5.687 0.596 0.974 0.971 15.17KENON40 1.582 −0.331 9.383 5.941 −0.128 0.894 0.881 23.89

2 Triton X-100 21.052 −0.466 5.483 6.443 0.233 0.785 0.757 39.123NP10 11.975 −0.309 5.359 10.359 0.0749 0.875 0.859 24.05KENON40 2.848 −0.294 6.294 20.319 0.142 0.856 0.837 20.1

Table 14Variance inflation factor for predictors of models Rønningsen, al-Roomi andmodified equation.

Predictors of Rønningsen model

T ϕ T�ϕ

VIF 21.167 7 27.167

Predictors of al-Roomi model

γ ϕ T

VIF 1 1 1

Predictors of modified model

γ ϕ T ω

VIF 1 1 1 1

M. Azodi, A.R. Solaimany Nazar / Journal of Petroleum Science and Engineering 106 (2013) 1–8 7

shows that this coefficient depends on factors such as oil andemulsifier type and emulsifier concentration that are not consid-ered in this model. Coefficient b is the power of shear rate inal-Roomi model. Negative value of this coefficient indicates thepseudo-plastic behavior of viscosity. Variation of γb is determined

within 0.0414oγbo0.509. Here c is the coefficient of oil concen-tration in the model. Positive value of this coefficient means thatthe oil viscosity increases with an increase in oil concentration.Experimental results (Figs. 1 and 2) indicate that the sign of thiscoefficient is correct. Variation of exp(cϕ) is determined within5.68oexp(cϕ)o56,919. The great variation of this term showsthat its value strongly depends on the oil and emulsifier type andconcentration of emulsifier. The variation of exp(d/T) term iscalculated within 1.2oexp(d/T)o10.4. As can be seen the varia-tion of this term with changing the oil and emulsifier type andemulsifier concentration is not great.

The variation of coefficients K1 in the modified model is within0.351oK1o21.052. The variation of this coefficient is less thanthat of the coefficient a in al-Roomi model. So, by addition ofemulsifier concentration to the modified model, the variation ofthese coefficients decreases. Coefficient n is the power of shearrate in the modified model with a negative value. Variation of γn iswithin 0.04oγno0.51. These results are very close to al-Roomiresults, and indicate that the emulsifier concentration dependencehas no significant effect on this term. The C1 is the coefficient of oilconcentration in the modified model. Variation of exp(c1ϕ) iscalculated within 8.5oexp(c1ϕ)o712. The variation range of thiscoefficient is very low compared to that of the coefficient c in al-Roomi model. Thus, including emulsifier concentration reducesthe variations of these coefficients. It is clear from the results that

M. Azodi, A.R. Solaimany Nazar / Journal of Petroleum Science and Engineering 106 (2013) 1–88

these variations are mostly dependent on oil types; therefore, theeffect of oil properties on this term is important. Variations of exp(d/T) are within 1.1oexp(c2T)o2.76. As observed, the variation ofthese terms decreases compared to the variation of exp(d/T) inal-Roomi model. The C3 is the coefficient of the emulsifier con-centration. The signs of these coefficients are positive that indicatethe viscosity increase as emulsifier concentration increases exceptfor one case indicated in Table 13.

4. Conclusion

In this study the laboratory investigation of the effective factorson the viscosity of two heavy crude oil types in water emulsion isdiscussed. These factors include three types of emulsifiers, emul-sifier concentration, oil concentration, salinity, mixing speed andtemperature and interactions. The oil concentration factor has thegreatest impact on viscosity of emulsions of both heavy crude oiltypes. The effect of temperature and emulsifier concentration isless than that of the effect of oil concentration. The effects of otherfactors and interactions on viscosity are far less with respect to theeffect of oil concentration.

A modified rheological equation is developed for predicting theviscosity of oil–water emulsion. The modified equation comparedwith the two existing rheological models fits better with viscosityof emulsions of both oil types' data. The signs and values of thecoefficients of the introduced modified equation give a betterdescription of the discussed factors effects.

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